I don't know about cigar boxes but:
Try AC Moores or Michaels for small little tiny "crafts brooms" for your "thatch". There was a pic of some on another forum, that's what reminded me of them.
Any round cardboard container will do. Depending on size you want here are some ideas: round salt box, round Stove Top Stuffing box, round Oatmeal box...that comes in two sizes.... they are "cheap and easy".
Then there is round pipes at the hardware store. THey come in several diameters too.
For the stone look I used to have links to stone wall photos that I can't find right off hand now that one could print off the computer and paste onto anything they wanted to give a stone look to. Try a google search for "stone wall photos". They come in a variety of stone sizes to choose from.
Hope this helps you.
EDIT: FOUND IT! here is the site that has photos or various surfaces you can print out and glue to your "stone structure":
pay particular attention to and click on the "brick" link, third over from "animals" there are also various stone walls there too.
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